Control and suppression of viscous fingering displacing non-Newtonian fluid with time-dependent injection strategies

We explore the stabilization mechanism of the fluid-fluid interface in the radial Hele-Shaw cell, displacing a non-Newtonian fluid. It is possible to stabilize the interface following a non-linear injection rate, Q similar to t(-(2 - n) / (2 + n)), which is related to the displaced fluid rheology (n : power-law index). This suggests the absence of fingering at constant injection when n similar to 2. We propose a quantitative criterion to control the pattern formation and suppress fingering, through the dimensionless parameter J as a function of the physical and operating parameters, which is applicable for a generalized shear thinning fluid. The parameter J is related to the capillary number in the context of the power-law fluid, relating to the viscous and interfacial forces. The fingering morphology at higher order modes is affected by non-linear effects. The results are non-intuitive, and we have shown a feasible approach toward long term fingering stabilization. Published under an exclusive license by AIP Publishing.

Automated summary

This study explores the stabilization mechanism of the fluid-fluid interface in the radial Hele-Shaw cell using a non-Newtonian fluid. It is found that the interface can be stabilized by a non-linear injection rate related to the rheology of the displaced fluid. A quantitative criterion, represented by the dimensionless parameter J, is proposed to control pattern formation and suppress fingering in shear thinning fluids.